Biomedical Engineering Reference
In-Depth Information
Similar to the reasoning for the characteristic equation for a differential equation, the cutoff
1
R
b
C
1
R
b
C
frequency is defined as o
c
¼
, (i.e., the denominator term,
j
o þ
is set equal to zero). Thus,
500
rad
s
1
R
b
C
¼
with the cutoff frequency set at o
c
¼
, then
500
:
The cutoff frequency is also defined
j ¼
M
The magnitude of
V
0
V
s
as when
j
Hj
ðÞ
p
, where
M
¼
5
:
is given by
1
R
a
C
¼
V
0
V
s
s
2
1
R
b
C
o
2
þ
500
rad
s
and at the cutoff frequency, o
c
¼
,
1
R
a
C
5
p ¼
s
2
1
R
b
C
o
2
c
þ
1
R
b
C
¼
With
500, the magnitude is
1
R
a
C
o
2
1
R
a
C
500
2
1
R
a
C
500
5
p ¼
s
¼
q
¼
p
2
500
2
1
R
b
C
þ
c
þ
which gives
1
2500
R
a
C
¼
1
2500
and
1
R
b
C
¼
Since we have three unknowns and two equations (
R
a
C
¼
500), there are an
infinite number of solutions. Therefore, one can select a convenient value for one of the
elements—say,
R
a
¼
20 k
O
—and the other two elements are determined as
1
2500
1
C
¼
R
a
¼
20000
¼
20 nF
2500
and
1
1
R
b
¼
C
¼
10
9
¼
100 k
O
500
500
20
A plot of the magnitude versus frequency is shown in the following figure. As can be seen, the
cutoff frequency gives a value of magnitude equal to 3.53 at 100 Hz, which is the design goal.
